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[[254,58,21]] d ≤
n
254
k
58
d
21
kd²/n
100.701
w
16

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Distance

d_X 21 · witness weight 21 (claimed upper_bound)
witness operator (support, 21 qubits)
[29, 60, 66, 78, 87, 91, 99, 100, 113, 122, 128, 134, 139, 154, 160, 166, 189, 197, 220, 229, 245]
d_Z 21 · witness weight 21 (claimed upper_bound)
witness operator (support, 21 qubits)
[19, 25, 32, 40, 79, 100, 109, 118, 121, 147, 172, 181, 196, 201, 208, 209, 214, 226, 227, 229, 234]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @seunomonije
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle (two-block) code on the cyclic group Z_127: H_X = [A|B], H_Z = [B^T|A^T] with A, B circulants; a(x) support {6,37,39,64,68,100,105,106} (weight 8), b(x) support {4,9,40,81,93,95,115,118} (weight 8), max check weight 16. Divisor trick: both a and b are sparse multiples of a degree-29 divisor g of x127-1 (x127-1 factors over GF(2) as (x+1) times eighteen degree-7 irreducibles; g here is (x+1) times four of the degree-7 factors, deg g = deg gcd(a,b,x127-1) = 29, machine-verified), locking k = 2*29 = 58 before any linear algebra. Distance evidence: rising RIS ladder 20k/100k/400k/1.6M/2M trials (fresh seed per rung) flat at d<=21 at every rung; refutation barrage 8M trials x 3 fresh seeds (777/999/424242) at pair_depth 16 plus 3M trials x same seeds at pair_depth 24 (33M further trials) all bottoming at exactly d<=21; the 2M-trial witness search returned the embedded weight-21 X logical, and the GB transpose symmetry (block swap + index reversal i -> -i mod 127) maps it to the embedded weight-21 Z logical, both machine-verified against ker/rowspace.
model Claude Claude Fable 5 (claimed, not verified)
date 2026-07-17
notes Search and verification by Claude Fable 5. First k=58 entry at n=254: beats [[254,44,24]] on kd^2/n (100.7 vs 99.8) and extends the n<=254 Pareto frontier in k (previous max k=44). Novelty vs the literature unverified. Deep-distance evidence: 16 sibling candidates from the same divisor sweep were laddered to 2M trials; this was the only one flat at 21 from 20k through 2M, and it survived a 33M-trial refutation barrage (3 seeds x 8M @ pair_depth 16, 3 seeds x 3M @ pair_depth 24) without moving.
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 127 · Z-checks 127
H_X (127 checks, sparse supports)
[6, 37, 39, 64, 68, 100, 105, 106, 131, 136, 167, 208, 220, 222, 242, 245] [7, 38, 40, 65, 69, 101, 106, 107, 132, 137, 168, 209, 221, 223, 243, 246] [8, 39, 41, 66, 70, 102, 107, 108, 133, 138, 169, 210, 222, 224, 244, 247] [9, 40, 42, 67, 71, 103, 108, 109, 134, 139, 170, 211, 223, 225, 245, 248] [10, 41, 43, 68, 72, 104, 109, 110, 135, 140, 171, 212, 224, 226, 246, 249] [11, 42, 44, 69, 73, 105, 110, 111, 136, 141, 172, 213, 225, 227, 247, 250] [12, 43, 45, 70, 74, 106, 111, 112, 137, 142, 173, 214, 226, 228, 248, 251] [13, 44, 46, 71, 75, 107, 112, 113, 138, 143, 174, 215, 227, 229, 249, 252] [14, 45, 47, 72, 76, 108, 113, 114, 139, 144, 175, 216, 228, 230, 250, 253] [15, 46, 48, 73, 77, 109, 114, 115, 127, 140, 145, 176, 217, 229, 231, 251] [16, 47, 49, 74, 78, 110, 115, 116, 128, 141, 146, 177, 218, 230, 232, 252] [17, 48, 50, 75, 79, 111, 116, 117, 129, 142, 147, 178, 219, 231, 233, 253] [18, 49, 51, 76, 80, 112, 117, 118, 127, 130, 143, 148, 179, 220, 232, 234] [19, 50, 52, 77, 81, 113, 118, 119, 128, 131, 144, 149, 180, 221, 233, 235] [20, 51, 53, 78, 82, 114, 119, 120, 129, 132, 145, 150, 181, 222, 234, 236] [21, 52, 54, 79, 83, 115, 120, 121, 130, 133, 146, 151, 182, 223, 235, 237] [22, 53, 55, 80, 84, 116, 121, 122, 131, 134, 147, 152, 183, 224, 236, 238] [23, 54, 56, 81, 85, 117, 122, 123, 132, 135, 148, 153, 184, 225, 237, 239] [24, 55, 57, 82, 86, 118, 123, 124, 133, 136, 149, 154, 185, 226, 238, 240] [25, 56, 58, 83, 87, 119, 124, 125, 134, 137, 150, 155, 186, 227, 239, 241] [26, 57, 59, 84, 88, 120, 125, 126, 135, 138, 151, 156, 187, 228, 240, 242] [0, 27, 58, 60, 85, 89, 121, 126, 136, 139, 152, 157, 188, 229, 241, 243] [0, 1, 28, 59, 61, 86, 90, 122, 137, 140, 153, 158, 189, 230, 242, 244] [1, 2, 29, 60, 62, 87, 91, 123, 138, 141, 154, 159, 190, 231, 243, 245] [2, 3, 30, 61, 63, 88, 92, 124, 139, 142, 155, 160, 191, 232, 244, 246] [3, 4, 31, 62, 64, 89, 93, 125, 140, 143, 156, 161, 192, 233, 245, 247] [4, 5, 32, 63, 65, 90, 94, 126, 141, 144, 157, 162, 193, 234, 246, 248] [0, 5, 6, 33, 64, 66, 91, 95, 142, 145, 158, 163, 194, 235, 247, 249] [1, 6, 7, 34, 65, 67, 92, 96, 143, 146, 159, 164, 195, 236, 248, 250] [2, 7, 8, 35, 66, 68, 93, 97, 144, 147, 160, 165, 196, 237, 249, 251] [3, 8, 9, 36, 67, 69, 94, 98, 145, 148, 161, 166, 197, 238, 250, 252] [4, 9, 10, 37, 68, 70, 95, 99, 146, 149, 162, 167, 198, 239, 251, 253] [5, 10, 11, 38, 69, 71, 96, 100, 127, 147, 150, 163, 168, 199, 240, 252] [6, 11, 12, 39, 70, 72, 97, 101, 128, 148, 151, 164, 169, 200, 241, 253] [7, 12, 13, 40, 71, 73, 98, 102, 127, 129, 149, 152, 165, 170, 201, 242] [8, 13, 14, 41, 72, 74, 99, 103, 128, 130, 150, 153, 166, 171, 202, 243] [9, 14, 15, 42, 73, 75, 100, 104, 129, 131, 151, 154, 167, 172, 203, 244] [10, 15, 16, 43, 74, 76, 101, 105, 130, 132, 152, 155, 168, 173, 204, 245] [11, 16, 17, 44, 75, 77, 102, 106, 131, 133, 153, 156, 169, 174, 205, 246] [12, 17, 18, 45, 76, 78, 103, 107, 132, 134, 154, 157, 170, 175, 206, 247] [13, 18, 19, 46, 77, 79, 104, 108, 133, 135, 155, 158, 171, 176, 207, 248] [14, 19, 20, 47, 78, 80, 105, 109, 134, 136, 156, 159, 172, 177, 208, 249] [15, 20, 21, 48, 79, 81, 106, 110, 135, 137, 157, 160, 173, 178, 209, 250] [16, 21, 22, 49, 80, 82, 107, 111, 136, 138, 158, 161, 174, 179, 210, 251] [17, 22, 23, 50, 81, 83, 108, 112, 137, 139, 159, 162, 175, 180, 211, 252] [18, 23, 24, 51, 82, 84, 109, 113, 138, 140, 160, 163, 176, 181, 212, 253] [19, 24, 25, 52, 83, 85, 110, 114, 127, 139, 141, 161, 164, 177, 182, 213] [20, 25, 26, 53, 84, 86, 111, 115, 128, 140, 142, 162, 165, 178, 183, 214] [21, 26, 27, 54, 85, 87, 112, 116, 129, 141, 143, 163, 166, 179, 184, 215] [22, 27, 28, 55, 86, 88, 113, 117, 130, 142, 144, 164, 167, 180, 185, 216] [23, 28, 29, 56, 87, 89, 114, 118, 131, 143, 145, 165, 168, 181, 186, 217] [24, 29, 30, 57, 88, 90, 115, 119, 132, 144, 146, 166, 169, 182, 187, 218] [25, 30, 31, 58, 89, 91, 116, 120, 133, 145, 147, 167, 170, 183, 188, 219] [26, 31, 32, 59, 90, 92, 117, 121, 134, 146, 148, 168, 171, 184, 189, 220] [27, 32, 33, 60, 91, 93, 118, 122, 135, 147, 149, 169, 172, 185, 190, 221] [28, 33, 34, 61, 92, 94, 119, 123, 136, 148, 150, 170, 173, 186, 191, 222] [29, 34, 35, 62, 93, 95, 120, 124, 137, 149, 151, 171, 174, 187, 192, 223] [30, 35, 36, 63, 94, 96, 121, 125, 138, 150, 152, 172, 175, 188, 193, 224] [31, 36, 37, 64, 95, 97, 122, 126, 139, 151, 153, 173, 176, 189, 194, 225] [0, 32, 37, 38, 65, 96, 98, 123, 140, 152, 154, 174, 177, 190, 195, 226] [1, 33, 38, 39, 66, 97, 99, 124, 141, 153, 155, 175, 178, 191, 196, 227] [2, 34, 39, 40, 67, 98, 100, 125, 142, 154, 156, 176, 179, 192, 197, 228] [3, 35, 40, 41, 68, 99, 101, 126, 143, 155, 157, 177, 180, 193, 198, 229] [0, 4, 36, 41, 42, 69, 100, 102, 144, 156, 158, 178, 181, 194, 199, 230] [1, 5, 37, 42, 43, 70, 101, 103, 145, 157, 159, 179, 182, 195, 200, 231] [2, 6, 38, 43, 44, 71, 102, 104, 146, 158, 160, 180, 183, 196, 201, 232] [3, 7, 39, 44, 45, 72, 103, 105, 147, 159, 161, 181, 184, 197, 202, 233] [4, 8, 40, 45, 46, 73, 104, 106, 148, 160, 162, 182, 185, 198, 203, 234] [5, 9, 41, 46, 47, 74, 105, 107, 149, 161, 163, 183, 186, 199, 204, 235] [6, 10, 42, 47, 48, 75, 106, 108, 150, 162, 164, 184, 187, 200, 205, 236] [7, 11, 43, 48, 49, 76, 107, 109, 151, 163, 165, 185, 188, 201, 206, 237] [8, 12, 44, 49, 50, 77, 108, 110, 152, 164, 166, 186, 189, 202, 207, 238] [9, 13, 45, 50, 51, 78, 109, 111, 153, 165, 167, 187, 190, 203, 208, 239] [10, 14, 46, 51, 52, 79, 110, 112, 154, 166, 168, 188, 191, 204, 209, 240] [11, 15, 47, 52, 53, 80, 111, 113, 155, 167, 169, 189, 192, 205, 210, 241] [12, 16, 48, 53, 54, 81, 112, 114, 156, 168, 170, 190, 193, 206, 211, 242] [13, 17, 49, 54, 55, 82, 113, 115, 157, 169, 171, 191, 194, 207, 212, 243] [14, 18, 50, 55, 56, 83, 114, 116, 158, 170, 172, 192, 195, 208, 213, 244] [15, 19, 51, 56, 57, 84, 115, 117, 159, 171, 173, 193, 196, 209, 214, 245] [16, 20, 52, 57, 58, 85, 116, 118, 160, 172, 174, 194, 197, 210, 215, 246] [17, 21, 53, 58, 59, 86, 117, 119, 161, 173, 175, 195, 198, 211, 216, 247] [18, 22, 54, 59, 60, 87, 118, 120, 162, 174, 176, 196, 199, 212, 217, 248] [19, 23, 55, 60, 61, 88, 119, 121, 163, 175, 177, 197, 200, 213, 218, 249] [20, 24, 56, 61, 62, 89, 120, 122, 164, 176, 178, 198, 201, 214, 219, 250] [21, 25, 57, 62, 63, 90, 121, 123, 165, 177, 179, 199, 202, 215, 220, 251] [22, 26, 58, 63, 64, 91, 122, 124, 166, 178, 180, 200, 203, 216, 221, 252] [23, 27, 59, 64, 65, 92, 123, 125, 167, 179, 181, 201, 204, 217, 222, 253] [24, 28, 60, 65, 66, 93, 124, 126, 127, 168, 180, 182, 202, 205, 218, 223] [0, 25, 29, 61, 66, 67, 94, 125, 128, 169, 181, 183, 203, 206, 219, 224] [1, 26, 30, 62, 67, 68, 95, 126, 129, 170, 182, 184, 204, 207, 220, 225] [0, 2, 27, 31, 63, 68, 69, 96, 130, 171, 183, 185, 205, 208, 221, 226] [1, 3, 28, 32, 64, 69, 70, 97, 131, 172, 184, 186, 206, 209, 222, 227] [2, 4, 29, 33, 65, 70, 71, 98, 132, 173, 185, 187, 207, 210, 223, 228] [3, 5, 30, 34, 66, 71, 72, 99, 133, 174, 186, 188, 208, 211, 224, 229] [4, 6, 31, 35, 67, 72, 73, 100, 134, 175, 187, 189, 209, 212, 225, 230] [5, 7, 32, 36, 68, 73, 74, 101, 135, 176, 188, 190, 210, 213, 226, 231] [6, 8, 33, 37, 69, 74, 75, 102, 136, 177, 189, 191, 211, 214, 227, 232] [7, 9, 34, 38, 70, 75, 76, 103, 137, 178, 190, 192, 212, 215, 228, 233] [8, 10, 35, 39, 71, 76, 77, 104, 138, 179, 191, 193, 213, 216, 229, 234] [9, 11, 36, 40, 72, 77, 78, 105, 139, 180, 192, 194, 214, 217, 230, 235] [10, 12, 37, 41, 73, 78, 79, 106, 140, 181, 193, 195, 215, 218, 231, 236] [11, 13, 38, 42, 74, 79, 80, 107, 141, 182, 194, 196, 216, 219, 232, 237] [12, 14, 39, 43, 75, 80, 81, 108, 142, 183, 195, 197, 217, 220, 233, 238] [13, 15, 40, 44, 76, 81, 82, 109, 143, 184, 196, 198, 218, 221, 234, 239] [14, 16, 41, 45, 77, 82, 83, 110, 144, 185, 197, 199, 219, 222, 235, 240] [15, 17, 42, 46, 78, 83, 84, 111, 145, 186, 198, 200, 220, 223, 236, 241] [16, 18, 43, 47, 79, 84, 85, 112, 146, 187, 199, 201, 221, 224, 237, 242] [17, 19, 44, 48, 80, 85, 86, 113, 147, 188, 200, 202, 222, 225, 238, 243] [18, 20, 45, 49, 81, 86, 87, 114, 148, 189, 201, 203, 223, 226, 239, 244] [19, 21, 46, 50, 82, 87, 88, 115, 149, 190, 202, 204, 224, 227, 240, 245] [20, 22, 47, 51, 83, 88, 89, 116, 150, 191, 203, 205, 225, 228, 241, 246] [21, 23, 48, 52, 84, 89, 90, 117, 151, 192, 204, 206, 226, 229, 242, 247] [22, 24, 49, 53, 85, 90, 91, 118, 152, 193, 205, 207, 227, 230, 243, 248] [23, 25, 50, 54, 86, 91, 92, 119, 153, 194, 206, 208, 228, 231, 244, 249] [24, 26, 51, 55, 87, 92, 93, 120, 154, 195, 207, 209, 229, 232, 245, 250] [25, 27, 52, 56, 88, 93, 94, 121, 155, 196, 208, 210, 230, 233, 246, 251] [26, 28, 53, 57, 89, 94, 95, 122, 156, 197, 209, 211, 231, 234, 247, 252] [27, 29, 54, 58, 90, 95, 96, 123, 157, 198, 210, 212, 232, 235, 248, 253] [28, 30, 55, 59, 91, 96, 97, 124, 127, 158, 199, 211, 213, 233, 236, 249] [29, 31, 56, 60, 92, 97, 98, 125, 128, 159, 200, 212, 214, 234, 237, 250] [30, 32, 57, 61, 93, 98, 99, 126, 129, 160, 201, 213, 215, 235, 238, 251] [0, 31, 33, 58, 62, 94, 99, 100, 130, 161, 202, 214, 216, 236, 239, 252] [1, 32, 34, 59, 63, 95, 100, 101, 131, 162, 203, 215, 217, 237, 240, 253] [2, 33, 35, 60, 64, 96, 101, 102, 127, 132, 163, 204, 216, 218, 238, 241] [3, 34, 36, 61, 65, 97, 102, 103, 128, 133, 164, 205, 217, 219, 239, 242] [4, 35, 37, 62, 66, 98, 103, 104, 129, 134, 165, 206, 218, 220, 240, 243] [5, 36, 38, 63, 67, 99, 104, 105, 130, 135, 166, 207, 219, 221, 241, 244]
H_Z (127 checks, sparse supports)
[9, 12, 32, 34, 46, 87, 118, 123, 148, 149, 154, 186, 190, 215, 217, 248] [10, 13, 33, 35, 47, 88, 119, 124, 149, 150, 155, 187, 191, 216, 218, 249] [11, 14, 34, 36, 48, 89, 120, 125, 150, 151, 156, 188, 192, 217, 219, 250] [12, 15, 35, 37, 49, 90, 121, 126, 151, 152, 157, 189, 193, 218, 220, 251] [0, 13, 16, 36, 38, 50, 91, 122, 152, 153, 158, 190, 194, 219, 221, 252] [1, 14, 17, 37, 39, 51, 92, 123, 153, 154, 159, 191, 195, 220, 222, 253] [2, 15, 18, 38, 40, 52, 93, 124, 127, 154, 155, 160, 192, 196, 221, 223] [3, 16, 19, 39, 41, 53, 94, 125, 128, 155, 156, 161, 193, 197, 222, 224] [4, 17, 20, 40, 42, 54, 95, 126, 129, 156, 157, 162, 194, 198, 223, 225] [0, 5, 18, 21, 41, 43, 55, 96, 130, 157, 158, 163, 195, 199, 224, 226] [1, 6, 19, 22, 42, 44, 56, 97, 131, 158, 159, 164, 196, 200, 225, 227] [2, 7, 20, 23, 43, 45, 57, 98, 132, 159, 160, 165, 197, 201, 226, 228] [3, 8, 21, 24, 44, 46, 58, 99, 133, 160, 161, 166, 198, 202, 227, 229] [4, 9, 22, 25, 45, 47, 59, 100, 134, 161, 162, 167, 199, 203, 228, 230] [5, 10, 23, 26, 46, 48, 60, 101, 135, 162, 163, 168, 200, 204, 229, 231] [6, 11, 24, 27, 47, 49, 61, 102, 136, 163, 164, 169, 201, 205, 230, 232] [7, 12, 25, 28, 48, 50, 62, 103, 137, 164, 165, 170, 202, 206, 231, 233] [8, 13, 26, 29, 49, 51, 63, 104, 138, 165, 166, 171, 203, 207, 232, 234] [9, 14, 27, 30, 50, 52, 64, 105, 139, 166, 167, 172, 204, 208, 233, 235] [10, 15, 28, 31, 51, 53, 65, 106, 140, 167, 168, 173, 205, 209, 234, 236] [11, 16, 29, 32, 52, 54, 66, 107, 141, 168, 169, 174, 206, 210, 235, 237] [12, 17, 30, 33, 53, 55, 67, 108, 142, 169, 170, 175, 207, 211, 236, 238] [13, 18, 31, 34, 54, 56, 68, 109, 143, 170, 171, 176, 208, 212, 237, 239] [14, 19, 32, 35, 55, 57, 69, 110, 144, 171, 172, 177, 209, 213, 238, 240] [15, 20, 33, 36, 56, 58, 70, 111, 145, 172, 173, 178, 210, 214, 239, 241] [16, 21, 34, 37, 57, 59, 71, 112, 146, 173, 174, 179, 211, 215, 240, 242] [17, 22, 35, 38, 58, 60, 72, 113, 147, 174, 175, 180, 212, 216, 241, 243] [18, 23, 36, 39, 59, 61, 73, 114, 148, 175, 176, 181, 213, 217, 242, 244] [19, 24, 37, 40, 60, 62, 74, 115, 149, 176, 177, 182, 214, 218, 243, 245] [20, 25, 38, 41, 61, 63, 75, 116, 150, 177, 178, 183, 215, 219, 244, 246] [21, 26, 39, 42, 62, 64, 76, 117, 151, 178, 179, 184, 216, 220, 245, 247] [22, 27, 40, 43, 63, 65, 77, 118, 152, 179, 180, 185, 217, 221, 246, 248] [23, 28, 41, 44, 64, 66, 78, 119, 153, 180, 181, 186, 218, 222, 247, 249] [24, 29, 42, 45, 65, 67, 79, 120, 154, 181, 182, 187, 219, 223, 248, 250] [25, 30, 43, 46, 66, 68, 80, 121, 155, 182, 183, 188, 220, 224, 249, 251] [26, 31, 44, 47, 67, 69, 81, 122, 156, 183, 184, 189, 221, 225, 250, 252] [27, 32, 45, 48, 68, 70, 82, 123, 157, 184, 185, 190, 222, 226, 251, 253] [28, 33, 46, 49, 69, 71, 83, 124, 127, 158, 185, 186, 191, 223, 227, 252] [29, 34, 47, 50, 70, 72, 84, 125, 128, 159, 186, 187, 192, 224, 228, 253] [30, 35, 48, 51, 71, 73, 85, 126, 127, 129, 160, 187, 188, 193, 225, 229] [0, 31, 36, 49, 52, 72, 74, 86, 128, 130, 161, 188, 189, 194, 226, 230] [1, 32, 37, 50, 53, 73, 75, 87, 129, 131, 162, 189, 190, 195, 227, 231] [2, 33, 38, 51, 54, 74, 76, 88, 130, 132, 163, 190, 191, 196, 228, 232] [3, 34, 39, 52, 55, 75, 77, 89, 131, 133, 164, 191, 192, 197, 229, 233] [4, 35, 40, 53, 56, 76, 78, 90, 132, 134, 165, 192, 193, 198, 230, 234] [5, 36, 41, 54, 57, 77, 79, 91, 133, 135, 166, 193, 194, 199, 231, 235] [6, 37, 42, 55, 58, 78, 80, 92, 134, 136, 167, 194, 195, 200, 232, 236] [7, 38, 43, 56, 59, 79, 81, 93, 135, 137, 168, 195, 196, 201, 233, 237] [8, 39, 44, 57, 60, 80, 82, 94, 136, 138, 169, 196, 197, 202, 234, 238] [9, 40, 45, 58, 61, 81, 83, 95, 137, 139, 170, 197, 198, 203, 235, 239] [10, 41, 46, 59, 62, 82, 84, 96, 138, 140, 171, 198, 199, 204, 236, 240] [11, 42, 47, 60, 63, 83, 85, 97, 139, 141, 172, 199, 200, 205, 237, 241] [12, 43, 48, 61, 64, 84, 86, 98, 140, 142, 173, 200, 201, 206, 238, 242] [13, 44, 49, 62, 65, 85, 87, 99, 141, 143, 174, 201, 202, 207, 239, 243] [14, 45, 50, 63, 66, 86, 88, 100, 142, 144, 175, 202, 203, 208, 240, 244] [15, 46, 51, 64, 67, 87, 89, 101, 143, 145, 176, 203, 204, 209, 241, 245] [16, 47, 52, 65, 68, 88, 90, 102, 144, 146, 177, 204, 205, 210, 242, 246] [17, 48, 53, 66, 69, 89, 91, 103, 145, 147, 178, 205, 206, 211, 243, 247] [18, 49, 54, 67, 70, 90, 92, 104, 146, 148, 179, 206, 207, 212, 244, 248] [19, 50, 55, 68, 71, 91, 93, 105, 147, 149, 180, 207, 208, 213, 245, 249] [20, 51, 56, 69, 72, 92, 94, 106, 148, 150, 181, 208, 209, 214, 246, 250] [21, 52, 57, 70, 73, 93, 95, 107, 149, 151, 182, 209, 210, 215, 247, 251] [22, 53, 58, 71, 74, 94, 96, 108, 150, 152, 183, 210, 211, 216, 248, 252] [23, 54, 59, 72, 75, 95, 97, 109, 151, 153, 184, 211, 212, 217, 249, 253] [24, 55, 60, 73, 76, 96, 98, 110, 127, 152, 154, 185, 212, 213, 218, 250] [25, 56, 61, 74, 77, 97, 99, 111, 128, 153, 155, 186, 213, 214, 219, 251] [26, 57, 62, 75, 78, 98, 100, 112, 129, 154, 156, 187, 214, 215, 220, 252] [27, 58, 63, 76, 79, 99, 101, 113, 130, 155, 157, 188, 215, 216, 221, 253] [28, 59, 64, 77, 80, 100, 102, 114, 127, 131, 156, 158, 189, 216, 217, 222] [29, 60, 65, 78, 81, 101, 103, 115, 128, 132, 157, 159, 190, 217, 218, 223] [30, 61, 66, 79, 82, 102, 104, 116, 129, 133, 158, 160, 191, 218, 219, 224] [31, 62, 67, 80, 83, 103, 105, 117, 130, 134, 159, 161, 192, 219, 220, 225] [32, 63, 68, 81, 84, 104, 106, 118, 131, 135, 160, 162, 193, 220, 221, 226] [33, 64, 69, 82, 85, 105, 107, 119, 132, 136, 161, 163, 194, 221, 222, 227] [34, 65, 70, 83, 86, 106, 108, 120, 133, 137, 162, 164, 195, 222, 223, 228] [35, 66, 71, 84, 87, 107, 109, 121, 134, 138, 163, 165, 196, 223, 224, 229] [36, 67, 72, 85, 88, 108, 110, 122, 135, 139, 164, 166, 197, 224, 225, 230] [37, 68, 73, 86, 89, 109, 111, 123, 136, 140, 165, 167, 198, 225, 226, 231] [38, 69, 74, 87, 90, 110, 112, 124, 137, 141, 166, 168, 199, 226, 227, 232] [39, 70, 75, 88, 91, 111, 113, 125, 138, 142, 167, 169, 200, 227, 228, 233] [40, 71, 76, 89, 92, 112, 114, 126, 139, 143, 168, 170, 201, 228, 229, 234] [0, 41, 72, 77, 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